Question

log3(x+1) + log3(x-1) = 3*log3(2)

Answer 1

ОДЗ
x+1>0
x-1>0

x>-1
x>1

x∈(1,+бесконечности)

$log_3(x+1) + log_3(x-1) = 3cdotlog_32\\log_3((x+1) cdot(x-1) )= log_32^3\\log_3((x+1) cdot(x-1) )= log_38\\(x+1)(x-1)=8\\x^2-1=8\\x^2=9\\x=pm3$

с учетом ОДЗ корень только х=3